{"id":"c545ec81-0d50-460d-847b-66d648bd55de","arxiv_id":"2412.09926","paper_version":1,"verdict":"REJECT","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":2,"one_line_summary":"Dark photon and dark Z contributions to J/ψ → e+e−φ are far below the experimental limit, making the channel insensitive to these mediators.","lead":"This paper calculates how often the rare decay J/ψ → e+e−φ happens and whether a dark photon or dark Z could make it noticeably more frequent. It finds the dark contributions stay tiny under current constraints, so this decay is unlikely to reveal those new particles.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The claimed M_X-independence of the NP rate is unsupported: the amplitudes as written omit 1/(q^2-M_X^2) propagators, which can resonate where m_{12}^2 or m_phi^2 approaches M_X^2.","rationale":"The reader's weakest assumption identifies the same chokepoint: the paper's own sentence about M_X-independence is not a derivation. The massless-propagator treatment is the condition on which the central claim rests. If the full propagators produce a substantial enhancement near q^2 = M_X^2, then the statement that constraints preclude an observable signal in J/psi -> e+e- phi is unsupported; if the full calculation still yields BR well below 1.2e-7 for all M_X, the conclusion survives, but the paper would need to show that. Regarding other aspects: the coupling benchmarks (epsilon = 2e-2, epsilon_Z = 1e-5) are asserted without a derivation from the cited constraints, but using an overly large epsilon would make the NP contribution an overestimate, so that does not threaten the 'no signal' direction. The SM EM amplitude is borrowed from cited work, so the new-physics content is what needs checking. Eq. (3) is also too garbled to verify independently, which reinforces the need for the concrete recalculation. I therefore agree with the reader and recommend keeping the REJECT verdict until the propagator issue is resolved.","tokens_in":8200,"tokens_out":18929,"duration_ms":233450,"concrete_test":"Recompute the NP branching ratio in Eq. (2) with the full vector-mediator propagator i(g_mu_nu - q_mu q_nu/M_X^2)/(q^2 - M_X^2 + i M_X Gamma_X) on each of the two legs of the electron line, using Gamma_X from Sec. 2, and scan M_X over 0.01-2.1 GeV plus a fine scan around m_phi, for epsilon = 2e-2 and epsilon_Z = 1e-5. Keep the BESIII m_{12}^2 and m_{23}^2 integration limits of Eqs. (7)-(10). If any M_X bin lifts the total BR above 1.2e-7, or even above the flat-curve value by more than an order of magnitude, the M_X-independence claim and the 'cannot observe' conclusion are falsified; if not, the massless approximation is a harmless numerical simplification.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 4 states that the NP contribution is independent of the new-state mass because the vertex Lorentz structure is similar and the width is much smaller than the mass. That is not a justification for a massless propagator. In the EM amplitude, each virtual photon carries a 1/q^2 factor; if a dark photon or dark Z is inserted in the same diagrams, the corresponding factors must be 1/(q^2 - M_X^2 + i M_X Gamma_X). The dark-photon amplitude M_A as written simply rescales both electron-line vertices by epsilon and keeps the EM propagators, and Figs. 2-3 are flat in M_X, exactly what a massless-propagator calculation predicts. Over the plotted range 0.2-4.5 GeV, one leg has q^2 = m_{12}^2, which equals M_X^2 for M_X below about 2.08 GeV = M_J/psi - m_phi; the other leg has q^2 = m_phi^2, so M_X near m_phi also sits near a pole. At these points the true amplitude is not suppressed, and the integrated branching ratio can differ from the flat curve by orders of magnitude. Since the paper's only new quantitative claim is that the NP rate cannot approach the BESIII limit, this missing mass dependence is load-bearing. A separate issue is that epsilon = 2e-2 appears to violate existing dark-photon constraints, but that would only strengthen the final conclusion, so it is not the principal concern.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper reproduces the SM prediction for J/psi -> e+e- phi (branching ratio 2.28e-8, dominated by EM transitions, hadronic loops negligible) and then estimates the additional contribution from a dark photon or dark Z, taking benchmark mixings epsilon=2e-2 and epsilon_Z=1e-5 from the author's earlier constraint analysis. Because the resulting total branching ratio remains below the BESIII upper limit 1.2e-7, the paper concludes that this decay channel cannot discriminate between the SM and these two dark-sector models. The NP estimate is built by rescaling the SM amplitude with factors epsilon or epsilon_Z while retaining the SM propagators, and the central quantitative claim is that the NP contribution is mass-independent and negligible.","tokens_in":8595,"tokens_out":11399,"duration_ms":118119,"significance":"The SM part of the paper is not new but is a clear reproduction of Ref. [30], and the demonstration that hadronic loops are suppressed is useful context. If a fully derived dark-photon/dark-Z amplitude had been computed correctly, the paper would provide a valuable null-result stating that J/psi -> e+e- phi cannot probe these mediators under current constraints. However, as it stands the NP calculation is a scaling exercise rather than a derivation, so the main claim is not established; the paper would need a substantial rewrite of Section 4 and a justification of the used couplings before the result could be relied upon.","major_comments":[{"comment":"The dark photon amplitude M_A in Eq. (2) is obtained from M_EM by multiplying each fermion-photon vertex by epsilon and keeping the denominators of the SM amplitude unchanged. This assumes 1/(q^2-M_X^2) is effectively 1/q^2 for every virtual line, but no such approximation is derived; the statement in Sec. 4 that the width of the new state is much smaller than its mass would not justify replacing the propagator by a massless one. In the plotted mass range, one virtual leg has q^2=m_12^2, which can equal M_X^2 for M_X below about 2.08 GeV, and another leg has q^2=m_phi^2, so M_X near m_phi is also near a pole. At these points the true dark-photon propagator is not suppressed and the integrated branching ratio can differ from the flat curves of Figs. 2 and 3 by orders of magnitude. Because the flatness of the curves is exactly the content of the 'no enhancement' conclusion, this is a load-bearing error.","section":"Sec. 4, Eq. (2), M_A, Figs. 2-3"},{"comment":"Equation (3) is not a usable expression for the dark Z contribution. It contains undefined objects (P_psi, P_phi, gbar_nu nu', C_W, and the relation of g_L and g_R to the couplings of Sec. 2), and the propagator-like factors i(P_psi_nu P_psi_nu'/M_x^2 - gbar_nu nu')/(P_psi^2+i Gamma_x M_x^2 - M_x^2) appear to place the external J/psi momentum on the internal line. The expression therefore cannot be derived from the Lagrangian of Sec. 2, and the dark Z result cannot be checked or reproduced. This is not a presentation issue; it is the whole dark Z calculation.","section":"Sec. 4, Eq. (3)"},{"comment":"The benchmark values epsilon=2e-2 and epsilon_Z=1e-5 are asserted rather than derived in this paper. The text refers to constraints 'discussed in Ref.' without completing the reference and then points to [31], but it does not show how the bounds in Ref. [31] translate into these specific values. Since the plotted NP rates are just the SM rates rescaled by these parameters, the conclusion that the NP contribution is far below the experimental limit is essentially a restatement of the input couplings. The paper should either derive the values or clearly frame the plots as a scan over representative points.","section":"Sec. 4 and Sec. 1"}],"minor_comments":[{"comment":"The abstract and Sec. 3 state a 'branching ratio' of 2.28e-8 keV; a branching ratio is dimensionless. Table 1 lists the width as 2.12e-6 keV and the branching ratio as 2.28e-8, so the unit should be removed.","section":"Abstract and Sec. 3"},{"comment":"The notation for the dark Z mixing parameter is inconsistent: epsilon_Z is used in Sec. 2, while Sec. 4 and the figure captions use epsilon' with epsilon'=1e-5; please unify the notation.","section":"Sec. 4"},{"comment":"The text says the M_X range is 'MB-MK and 2m_mu', but Figs. 2-3 extend from 0.2 to 4.5 GeV; the exact scanned range and the rationale for the gaps around the phi and J/psi masses need to be stated.","section":"Sec. 4"},{"comment":"The sentence 'All these constraints were discussed in Ref.' is incomplete and should give the reference number and a short summary of the constraints.","section":"Sec. 1"},{"comment":"The hadronic loop contributions are presented only through effective couplings and a table; since one of the paper's claims is that hadronic effects are negligible, a reference to the explicit loop amplitudes (or an appendix) is needed to make the table reproducible.","section":"Sec. 3"}],"recommendation":"major_revision","confidential_remarks":"The paper is essentially an application of the author's previous constraint analysis [31] to one decay mode. The main result, if correct, is a negative statement. I would only consider publication after the NP amplitudes are derived from the Lagrangian, the propagator issue is resolved, and the benchmark couplings are justified; in the present form the technical problems are too extensive for a routine revision."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Here's the short version: the SM part of this paper is fine—it reproduces Ref. [30]'s calculation of J/ψ→e+e−φ and confirms hadronic loops are negligible. The only new claim is that dark photon and dark Z contributions can't lift the branching ratio to the BESIII limit. That's probably true, but the calculation as presented doesn't support it.\n\nThe dark photon amplitude is just the EM amplitude with each vertex multiplied by ε and the same 1/q² photon propagators. That's a massless-propagator approximation, and the paper doesn't justify it. The statement in Sec. 4 that the NP contribution is independent of M_X because the vertex structure is similar and the width is small is simply not an argument. In the plotted M_X range, the invariant mass of the e+e− pair runs from threshold up to about 2.08 GeV, and m_φ is about 1.02 GeV, so for M_X in this range the propagator 1/(q²−M_X²) can pass through a pole. The true rate won't be flat in M_X, and the sensitivity conclusion could change by orders of magnitude near those points. That's load-bearing, because the entire NP section exists to make that negative statement.\n\nThere's also a practical issue: Eq. (3), the dark Z amplitude, is garbled—undefined symbols (Pψ, ¯g, etc.) and inconsistent Lorentz structure. And the benchmarks ε=2×10⁻² and εZ=10⁻⁵ are asserted rather than derived; at least ε=2×10⁻² looks like it's already excluded by dedicated dark photon searches, though if so that only strengthens the paper's point.\n\nWhat's genuinely useful: the SM prediction and the demonstration that this channel is a clean probe. That part is worth citing. But the NP analysis is not in a publishable state. I'd desk reject with an invitation to resubmit after deriving the full amplitude with massive mediators and comparing to actual limits. There's a real, modest result in here—it just isn't in this version.","headline":"The negative dark-sector result is probably right, but the calculation as written doesn't show it: the new-state propagator is dropped without justification, and Eq. (3) is garbled.","tokens_in":9029,"tokens_out":3871,"would_cite":false,"duration_ms":36949,"reading_group":"no","serious_thinker":"no","would_accept_peer_review":false},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The rare decay $J/psi \\to e^+e^-\\phi$ cannot expose a dark photon or dark $Z$: allowed mixing keeps the new-physics signal below the experimental sensitivity.","keywords":["charmonium decay","dark photon","dark Z","vector meson dominance","rare decay","branching ratio","Standard Model","new physics"],"falsifier":"Look for a narrow enhancement in the $e^+e^-$ invariant-mass distribution of $J/\\psi \\to e^+e^-\\phi$ at a high-statistics experiment, or a branching ratio approaching the $1.2 \\times 10^{-7}$ upper limit; either would contradict the paper's claim that no dark photon or dark $Z$ signal is observable. Equivalently, recompute the amplitude with a finite mediator mass $M_x$ and check whether any allowed mass makes the total branching ratio reach the experimental limit.","tokens_in":8000,"feed_emoji":"⚛️","tokens_out":11990,"duration_ms":113678,"temperature":0.7,"pith_summary":"The paper asks whether the rare decay $J/\\psi \\to e^+e^-\\phi$ could expose a neutral state from a dark sector: a dark photon or a dark $Z$. It computes the Standard Model branching ratio to be about $2.28 \\times 10^{-8}$, dominated by electromagnetic transitions through vector meson dominance, with hadronic loop contributions from $f_0(980)$, $\\eta$, and $\\eta'$ smaller by at least three orders of magnitude. It then adds dark photon and dark $Z$ amplitudes at the largest mixing values current constraints allow, $\\varepsilon = 2 \\times 10^{-2}$ and $\\varepsilon_Z = 10^{-5}$, and finds the total branching ratio stays far below the experimental upper limit of $1.2 \\times 10^{-7}$. The paper concludes that, with present data, this channel cannot distinguish the Standard Model from these two dark-sector models, so observing a signal from them here is out of reach.","feed_headline":"Rare J/psi decay can't reveal dark photon or dark Z","feed_subtitle":"Even at maximal allowed mixing, the predicted dark-sector signal stays far below the current experimental limit.","key_machinery":"The machinery is the $J/\\psi \\to e^+e^-\\phi$ transition amplitude built from vector meson dominance: the $J/\\psi$ and $\\phi$ each couple to a virtual photon through effective couplings $g_{\\psi\\gamma}$ and $g_{\\phi\\gamma}$, and the photon converts into the $e^+e^-$ pair. The dark photon and dark $Z$ amplitudes take the same Lorentz structure as the electromagnetic amplitude, with each fermion-photon vertex replaced by an $\\varepsilon$- or $\\varepsilon_Z$-scaled vertex and with the dark mediator propagator treated as effectively massless. Because of that similarity and because the dark-state width is far smaller than its mass, the new-physics rate is independent of the mediator mass $M_x$ over the range $2m_\\mu \\lesssim M_x \\lesssim M_B - M_K$ considered here. The result is a tiny additive shift to the SM branching ratio that current constraints prevent from reaching the experimental limit.","core_discovery":"The central result is a null result with a specified mechanism. The SM amplitude for $J/\\psi \\to e^+e^-\\phi$ is determined by vector-meson-dominance couplings $g_{\\psi\\gamma} = 0.150~\\mathrm{GeV}^2$ and $g_{\\phi\\gamma} = 0.013~\\mathrm{GeV}^2$, yielding a branching ratio of about $2.28 \\times 10^{-8}$, while hadronic loops are suppressed by more than three orders of magnitude. The dark photon and dark $Z$ amplitudes are copies of this electromagnetic amplitude with each photon-fermion vertex rescaled by $\\varepsilon$ or by the dark-$Z$ couplings, and at the benchmark values $\\varepsilon = 2 \\times 10^{-2}$ and $\\varepsilon_Z = 10^{-5}$ the total branching ratio remains essentially unchanged. Because existing constraints on the mixing parameters are so tight, the paper concludes that a large enhancement up to the experimental limit of $1.2 \\times 10^{-7}$ is not possible, making this decay an unpromising discovery channel for the dark photon and dark $Z$.","pith_inferences":["Beyond the paper: computing the dark photon or dark $Z$ amplitude with a finite mediator mass, especially near the $J/\\psi$ mass, could change both the rate and the invariant-mass shape even if the integrated effect stays small.","Beyond the paper: the same vertex-rescaling treatment applies to lepton-flavored analogs such as $J/\\psi \\to \\mu^+\\mu^-\\phi$, so the null conclusion likely carries over to those channels while the constraints remain unchanged.","Beyond the paper: because the dark $Z$ couplings are chiral, angular or Dalitz-plot observables might discriminate it from the Standard Model even at the same total rate; the paper integrates over the full rate and does not test this."],"forward_implications":["The Standard Model prediction for $J/\\psi \\to e^+e^-\\phi$ is stable at about $2.28 \\times 10^{-8}$, since hadronic loop contributions are suppressed by more than three orders of magnitude.","The experimental limit of $1.2 \\times 10^{-7}$ is only about five times the SM rate, yet dark photon and dark $Z$ contributions at currently allowed mixing stay far below that five-fold headroom.","Observing a signal from either dark state in this channel would require mixing parameters that are already excluded, so a positive detection is not expected.","If an excess is observed, it would have to come from a different new-physics mechanism rather than the dark photon or dark $Z$ as modeled here."],"supporting_citations":[{"why":"Supplies the Standard Model calculation of J/psi to e+e- phi, including VMD amplitudes and hadronic loop contributions, that sets the baseline rate.","marker":"[30]"},{"why":"Introduces the kinetic-mixing dark photon model whose coupling epsilon is used for the new-physics amplitude.","marker":"[5]"},{"why":"Defines the dark Z model through mass mixing and provides its couplings and decay phenomenology.","marker":"[7]"},{"why":"Supplies the updated constraints on epsilon and epsilon_Z that set the benchmark values and the allowed mass range.","marker":"[31]"},{"why":"Establishes vector meson dominance as the reason electromagnetic transitions dominate the SM rate.","marker":"[4]"},{"why":"Provides hadronic decay widths of light vector mediators used for the dark-state width in the rate calculation.","marker":"[28]"},{"why":"Supplies the measured R_H ratio used to convert the dark photon's leptonic width into a hadronic width.","marker":"[29]"}],"fun_headline_variants":["J/psi decay can't reveal dark photon or dark Z","Dark photon and dark Z stay hidden in J/psi decay","Search for dark sector in J/psi decay comes up empty","Rare J/psi decay offers no window for dark photon"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The calculation assumes the new particle acts as a massless mediator, so the dark photon and dark $Z$ rates do not depend on the mediator mass; if the mass is comparable to the momenta in the decay, the rates and the sensitivity conclusion could change.","fun_headline_variants_meta":{"raw":{"variants":["J/psi decay can't reveal dark photon or dark Z","Dark photon and dark Z stay hidden in J/psi decay","Search for dark sector in J/psi decay comes up empty","Rare J/psi decay offers no window for dark photon"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000255,"raw_usage":{"total_tokens":1589,"prompt_tokens":980,"completion_tokens":609,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":596,"completion_tokens_details":{"reasoning_tokens":538}},"tokens_in":596,"tokens_out":609,"duration_ms":5704,"temperature":1.0,"reasoning_tokens":538,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-11T16:34:36.217522+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Look for a narrow enhancement in the $e^+e^-$ invariant-mass distribution of $J/\\psi \\to e^+e^-\\phi$ at a high-statistics experiment, or a branching ratio approaching the $1.2 \\times 10^{-7}$ upper limit; either would contradict the paper's claim that no dark photon or dark $Z$ signal is observable. Equivalently, recompute the amplitude with a finite mediator mass $M_x$ and check whether any allowed mass makes the total branching ratio reach the experimental limit.","supporting_citations":[{"cited_title":"Study of the rare decay $J/\\psi\\rightarrow e^+e^- \\phi$","cited_arxiv_id":"1512.04149","evidence_quote":"Supplies the Standard Model calculation of J/psi to e+e- phi, including VMD amplitudes and hadronic loop contributions, that sets the baseline rate."},{"cited_title":"Guberina, J.H","cited_arxiv_id":null,"evidence_quote":"Establishes vector meson dominance as the reason electromagnetic transitions dominate the SM rate."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the measured R_H ratio used to convert the dark photon's leptonic width into a hadronic width."}],"review_version":1}